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- 1. INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2003; 27:1067–1078 (DOI: 10.1002/er.936) Exergy losses in refrigerating systems. A study for performance comparisons in compressor and condenser A. Stegou-Sagian,y and N. Paignigiannis Department of Mechanical Engineering, Thermal Section, National Technical University of Athens, 9 Iroon Polytechniou Str., Zografou 15780, Athens, Greece SUMMARYA study is carried out to describe irreversibilities in one stage refrigerating process for vapourcompression cycle with refrigerant mixtures R-404A, R-410A, R-410B and R-507 as working ﬂuids. Theyare calculated as exergy losses by an algorithm developed on the basis of thermodynamics. The pro-posed relationships have been derived from exergy balances on the system components. Emphasis isplaced on parameters inﬂuencing the losses and the related results are presented through Grassmanndiagrams (diagrams of exergy ﬂuxes). Furthermore, detailed information on the variation of cycle’sexergy eﬃciency with evaporating and condensing temperatures is given. Copyright # 2003 John Wiley &Sons, Ltd.KEY WORDS: exergy; refrigerating systems; ozone friendly mixtures 1. INTRODUCTIONAll forms of energy consist of two components: exergy and anergy (Baehr, 1989), i.e.: Energy ¼ Exergy þ Anergy ð1ÞThe term of exergy was introduced so that the limited ability of energy transformation isdemonstrated. Taking the ability of energy transformation as a criterion of selection, energy forms aredivided in the following groups: * energy that can be converted without any limitations, like mechanical or electrical energy; * energy that can be limitedly converted, like heat or internal energy; * energy that cannot be converted, like environmental internal energy. All known thermodynamic theorems can be expressed so as to include the term of exergy. Asa result, the First Thermodynamic law has the following formulation: In all processes, the sumof exergy and anergy remains constant. Additionally, for the Second Thermodynamic law then Correspondence to: Dr. Athina Sagia, Department of Mechanical Engineering, Thermal Section, National Technical University of Athens, 9 Iroon Polytechniou Str., Zografou 15780, Athens, Greece.y E-mail: asagia@central.ntua.gr Received 5 November 2002Copyright # 2003 John Wiley & Sons, Ltd. Accepted 5 March 2003
- 2. 1068 A. STEGOU-SAGIA AND N. PAIGNIGIANNISmain expressions are: * In all irreversible processes, exergy is converted into anergy. * In reversible processes, exergy remains constant. * It is imposible to convert anergy into exergy. Exergy losses are inevitable because all natural processes are irreversible. Technically andeconomically speaking, exergy is valuable, and as a consequence, whenever we try to solve aproblem through the scope of exergy analysis, we try to ﬁnd a speciﬁc exergy loss, whichminimizes operational costs. In this article, the optimization of one stage refrigerating systems through exergy analysis wasof paramount importance. The assumption is, that the refrigeration cycle works between thetemperature of a refrigerated space To and the ambient Tu : The kind of refrigerant used and theoperating conditions are the key factors for our study. The development of environmentally benign refrigerants remains a fundamental issuenowadays (Cavallini, 1995; ASHRAE, 1997; Blackmore and Reddish, 1996; Ozone Secretariat,2000); it may be enhanced with useful comparisons on the distribution of exergy losses and onthe eﬃciency values of vapour compression refrigerating cycles working with ozone friendlymixtures such as R-404A, R-410A, R-410B and R-507. All these four (4) refrigerant mixturesare characterized by a zero Ozone Depletion Potential (ODP) coeﬃcient, thus they do notcontribute to the depletion of the ozone layer. Their per cent weight compositions can be seen inTable I. 2. EXERGY ANALYSIS ASPECTSExergy (E) of an amount of heat (Q) may be deﬁned as (Smith and Van Ness, 1975; Baehr,1989): Tu E ¼ 1À Q ð2Þ TQwhere E; Q in (J) and Tu is the ambient temperature and TQ the temperature at which Q isabsorbed (heat sink) or rejected by theÁenvironment (heat source) in (K). À Below ambient temperature TQ 5Tu ; the heat amount (Q) will have a negative sign, as it isremoved from the space or substance which is cooled (for example a cold storage). Thus, EðQÞ isalways a positive quantity. Table I. The per cent weight composition of the refrigerant mixtures used in this study.Name of refrigerant mixture Percentage of ingredients (%) R-22 R-32 R-115 R-125 R-134a R-143aR-404A 44 4 52R-410A 50 50R-410B 45 55R-507 50 50R-502 48.8 51.2Copyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 3. EXERGY LOSSES IN REFRIGERATING SYSTEMS-A STUDY 1069 The exergy of the enthalpy of a process ﬂuid (e.g. a refrigerant) is calculated by (Baehr, 1989;Moran and Shapiro, 1993): ex ¼ ðhx À hu Þ À Tu ðsx À su Þ ð3Þwhere e is the speciﬁc exergy in (J/kg), while x and u stand for current and ambient conditions,respectively. Hence, exergy loss for a steady-state process including mass ﬂows (mj ), heat (Qj ) and work(Wj ) passing through the system boundaries is determined by: X X X DEloss ¼ Ein À Eout ¼ EðQj Þ þ Wj þ mj ej ð4ÞBy refrigeration, we aim to reduce the temperature of a cold storage space (To ) below theenvironmental temperature (Tu ). Because of the temperature diﬀerence ðTu À To Þ; an incomingheat ﬂux enters the cold storage space. In order to keep To constant, the incoming heat ﬂux mustbe constantly replaced by an outgoing heat ﬂux. This outgoing heat ﬂux stands for the coolingload. The depiction of a refrigerating engine is given at Figure 1. Q ¼ Q þ P ð5Þ o where Qo stands for the cooling load, Q for the rejected heat and P for the power givenat the compressor motor. Figure 2 shows the exergy ﬂux for an irreversible refrigerationsystem. The drawbacks of irreversibilities are the following: * increase in power demand; * increase in the anergy ﬂux rejected, which results in an increase of the cost of the refrigeration system, as larger heat exchangers are required.The exergy ﬂux is calculated by (Baehr, 1989; Moran and Shapiro,1993): Tu E Qo ¼ À 1 Qo ð6Þ To Figure 1. Refrigerating system. 1 ¼ Q; 2 ¼ Qo ; Q ¼ Qo þ P : Copyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 4. 1070 A. STEGOU-SAGIA AND N. PAIGNIGIANNIS Figure 2. Diagram for an irreversible refrigeration system (1 ¼ E Qo stands for the exergy of cooling load, while 2 ¼ B Qo denotes the anergy, 3 ¼ Eu ¼ Exergy lossesÞ:and the anergy Tu B Qo ¼ Qo ð7Þ ToAs we can see in Figure 2, power P can be calculated by P ¼ E Qo þ E u ð8Þ The term Eu refers to exergy losses. The eﬃciency or exergy eﬃciency factor (z) is a clear indication of the refrigerating cycle’sperformance. The exergy eﬃciency factor is deﬁned as follows: E Qo z¼ ð9Þ E Qo þ EuFigure 3 presents the key points of the one stage vapour compression refrigerating cycles. Forsimplicity reasons, we will assume that there is neither subcooling nor superheating of thesuctioned vapour. The pair of points: 2–3 (discharge line pressure drop), 4–7 (liquid line pressuredrop), 6–1 (suction line pressure drop) have almost similar entropy values. This viewpoint has been reached after extended parametric study. Using the theory encountered in (Baehr, 1989; Moran and Shapiro, 1993; Holman, 1997), theexergy losses occurring in all four (4) phases of the one stage refrigeration process are calculatedas follows: * Compression losses: Eu12 ¼ m Tu ðs2 À s1 Þ ð10ÞExergy losses due to the compressor motor (air-cooled compressor) may be included for a betteraccuracy. These losses are calculated as follows: 1 À nmotor Eumotor ¼ Pcompression ð11Þ nmotorCopyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 5. EXERGY LOSSES IN REFRIGERATING SYSTEMS-A STUDY 1071Figure 3. Pressure–enthalpy diagram for one stage vapour compression refrigerating cycle where12: compression (suction of no superheated vapour) 34: Desuperheating, condensation, 4: no subcooling,75: throttling, 56: evaporation. Pressure drops: 23 discharge line, 34 condenser, 47 liquid line, 56 evaporation, 61 suction line.So the total compression losses are: Eucompression ¼ Eu12 þ Emotor ð12Þ * Condensation and desuperheating losses: Eucd ¼ Qcondensation þ Qdesuperheating À m Tu ðs3 À s4 Þ ð13Þ * Throttling losses: Euthrottling ¼ m Tu ðs5 À s7 Þ ð14Þ * Evaporation losses: Euevaporation ¼ m Tu ðs6 À s5 Þ À E Qo À Qo ð15ÞThe total exergy losses are given by Eu ¼ Eucompression þ Euevaporation þ Eucd þ Euthrottling ð16Þ 3. EFFICIENCY AND GRASSMANN DIAGRAMS AS A FUNCTION OF OPERATING CONDITIONSA simulation program has been developed for the prediction of a refrigerating system eﬃciencyrelated to the condenser’s and evaporator’s temperature. The necessary thermodynamic properties such as equilibrium data, enthalpy and entropyvalues are calculated by Perry and Green, (1984), Reid et al. (1988), ICI Chemicals andPolymers (1995), NIST REFPROP (1996) and equations proposed by Stegou-Sagia (1997),Stegou-Sagia and Damanakis (1999) and Stegou-Sagia and Damanakis (2000). ComparisonsCopyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 6. 1072 A. STEGOU-SAGIA AND N. PAIGNIGIANNIShave been made with results calculated by Coolpack Software (2001) and the diﬀerencesobserved were minimal. We also have to note that all the calculated enthalpy and entropy valuestook into consideration the International Institute of Refrigeration standards, according towhich enthalpy and entropy values of 200 and 1 J/kgK, respectively occur at the state ofsaturated water of 0 8C. Exergy eﬃciency diagrams are chosen to be drawn bearing in mind the followingassumptions: * environmental temperature (Tu ) is equal to 20 8C; * isentropic compression eﬃciency (nis ) is equal to 0.75. * compressor motor eﬃciency (nmotor ) is equal to 1. * pressure drop in evaporator is equal to 10 K. * pressure drop in condenser is equal to 10 K. * pressure drop in suction line, discharge line and liquid line is equal to 0.2 bar. * the temperature of the cold space is 2 8C higher than that of the evaporation n temperature (To ). The diagrams of exergy eﬃciency for the alternative refrigerant mixtures under considerationare plotted in comparison with the corresponding conventional ones. More speciﬁcally, the plotsof exergy eﬃciency related to the evaporator’s temperature have been made for a constantcondensation temperature of 30 oC, while the evaporation temperature varies within the rangeof À5 to –40 8C. Also, the diagrams related to the condensation temperature have been drawnfor a constant evaporation temperature of À20 8C and the condensation temperature varieswithin the range of 25–60 8C. In order to create the exergy eﬃciency diagrams, we used the following methodology: Bysubstituting Equations (6) and (8) into Equation (9), we have: À Á À Á Tu =To À 1 Qo Tu =To À 1 Qo E Qo z¼ ¼ ð17Þ E Qo þ E P Psince the cooling load is always an incoming heat ﬂux to the evaporator. However, all refrigerating systems are characterized by a speciﬁc coeﬃcient of performance(COP), which is equal to the ratio of the cooling load to the power given at the compressormotor. Therefore, we get Tu z¼ À 1 COP ð18Þ ToFor every selected pair of evaporation and condensation temperatures and given all the above-mentioned assumptions (all of them were used as input to the software), we were able tocalculate the exergy eﬃciency factor through Equation (18) for the selected refrigerant mixturesand plot it for all the selected temperature ranges. Particular attention is paid to the fact that the working ﬂuids are non-azeotropic refrigerantmixtures and show diﬀerent behaviour from pure substances; the pressure–temperature curvefor saturated liquid is diﬀerent from that for vapour. This is taken into account in all relevantcalculations. The system design path, due to diﬀerent evaporator’s and condenser’s inlet/outletCopyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 7. EXERGY LOSSES IN REFRIGERATING SYSTEMS-A STUDY 1073temperature includes: * selection of evaporator’s outlet against the desired cold space temperature; * condenser inlet and outlet temperatures should be suﬃcient to reject heat; * liquid enthalpy at expansion device and related property data (NIST, 1996; ASHRAE, 1997) can be used to get evaporator’s inlet temperature. At all other points in the system, the ﬂuid behaves as normal. For the Grassmann plots, we have used the same basic assumptions as in exergy eﬃciencydiagrams. Furthermore: * the evaporation temperature which has been chosen equals À20 8C. * the compressor motor eﬃciency equals 0.85. * the cooling load equals 100 kW. In order to calculate the exergy eﬃciency factors and create the Grassmann plots, wecalculated the ratio of all exergy losses involved (as expressed in Equations (10)–(15)) to the incoming to the compressor motor exergy ﬂux (E Qo þ Eu ). 4. RESULTS4.1. Exergy eﬃciency diagramsBased on the above-mentioned assumptions and in order to compare the exergy eﬃciency factorsfor the refrigerant mixtures in question, we have drawn the exergy eﬃciency diagrams presented inFigures 4 and 5. Figure 4 correlates the exergy eﬃciency factor with the condensation temperaturefor constant evaporation temperature, whereas Figure 5 plots the exergy eﬃciency factor and theevaporation temperature for constant condensation temperature. As far as the exergy eﬃciency diagram for constant evaporation temperature is concerned, weobserve that for an increasing condensation temperature, the exergy eﬃciency factor isconstantly decreasing. This is absolutely explainable since, the evaporation temperature (To n)being constant, so is the temperature of the cold space (To ), according to the assumption alreadymade. Taking into account the fact that the ambient temperature has also been considered to beconstant, we can easily conclude that the Tu =To ratio remains constant. Thus, according to Equation (18), the exergy eﬃciency factor is only proportionate to theCOP. But according to theory, for a constant evaporation temperature, an increase of thecondensation temperature ultimately results in a decrease of the COP value, since a biggerpower of compression is needed. Consequently, and always in accordance with Equation (18),the COP decreasing, the exergy eﬃciency factor is also proportionately decreased. Based on Figure 4, we see that the conventional refrigerants generally present smaller exergylosses (for example, R-22 has the best exergy behaviour of all with an exergy eﬃciency of51.11% at a condensation temperature of 25 8C). This advantage is, however, counterbalancedby their detrimental environmental eﬀect (according to Montreal Protocol 2000, R-22 ischaracterized by an ODP of 0.055 compared to the zero ODP factors of R-404A, R-410A,R-410B and R-507). Regarding Figure 5, the exergy eﬃciency plots have a non-symmetrical bell-shaped form,attaining their maximum value at an evaporation temperature of either –25 or –20 8C, whereasCopyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 8. 1074 A. STEGOU-SAGIA AND N. PAIGNIGIANNIS Comparison of exergy efficiency factors (Evaporation temperature = -20°C) 0.55 0.50 0.45 0.40 Exergy efficiency 0.35 0.30 0.25 0.20 0.15 25 30 35 40 45 50 55 60 Condensation temperature (°C) R-22 R-502 R-410A R-410B R-507 R-404AFigure 4. Comparison of the energy eﬃciency factors for the refrigerant mixtures in question (R-404A,R-410A, R-410B and R-507) and their corresponding conventional ones (R-22 and R-502) for a constant evaporation temperature of À20 8C.the minimum value for all refrigerants is observed at an evaporation temperature of –5 8C.In this case, the Tu =To ratio does not remain constant and consequently, the exergy eﬃciencyfactor is dependent on both this ratio and the COP factor. Both these factors have a diﬀerentbehaviour for a constant condensation temperature and a continuously increasing evaporationtemperature (as an absolute value): the Tu =To ratio keeps increasing, whereas the COP valuekeeps decreasing. Thus, we cannot predict the exact form of the plots in advance. R-22maintains the best exergy behaviour and has an exergy eﬃciency factor slightly exceeding 45%at an evaporation temperature of À25 8C.4.2. Grassmann diagramsThe calculations supporting the drawing of the Grassmann diagrams for the four (4)environmentally friendly refrigerant mixtures in question were performed with the help ofCoolpack software. The above-mentioned Grassmann diagrams are depicted in Figures 6–9. From the drawn Grassmann diagrams, we can conclude that the biggest occurringexergy losses are those of compression, ranging from 34.3% (for R-410A) to 36% (forR-404A). Compression exergy losses are followed by condensation exergy losses, which varyCopyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 9. EXERGY LOSSES IN REFRIGERATING SYSTEMS-A STUDY 1075 Comparison of exergy efficiency factors (Condensation temperature = 30°C) 0. 46 0. 45 0. 44 Exergy efficiency 0. 43 0. 42 0. 41 0. 40 -40 -35 -30 -25 -20 -15 -10 -5 Evaporation temperature (°C) R-22 R- 502 R-410A R-410B R- 507 R-404AFigure 5. Comparison of the exergy eﬃciency factors for the refrigerant mixtures in question (R-404A,R-410A, R-410B and R-507) and their corresponding conventional ones (R-22 and R-502) for a constant condensation temperature of 30 8C. Figure 6. Grassmann diagram depicting the exergy losses with the use of R-404A.Copyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 10. 1076 A. STEGOU-SAGIA AND N. PAIGNIGIANNIS Figure 7. Grassmann diagram depicting the exergy losses with the use of R-410A. Figure 8. Grassmann diagram depicting the exergy losses with the use of R-410B. Figure 9. Grassmann diagram depicting the exergy losses with the use of R-507.from 12.3% (for R-404A) to 15.4% (for R-410A and R-410B). The third biggest exergylosses are those of evaporation, followed by throttling losses, both having values of lessthan 10%. The biggest exergy eﬃciency occurs with R-410A (39%). Additionally, we note that mixtureswith very similar compositions (like R-410A and R-410B) demonstrate similar exergybehaviour.Copyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 11. EXERGY LOSSES IN REFRIGERATING SYSTEMS-A STUDY 1077 Exergy losses occurring in all four (4) phases of the one stage refrigerating process can bereduced by modifying and/or improving the refrigerating system’s equipment. For example, thehigh-compression exergy losses could be diminished by using a more expensive compressor witha higher isentropic compression eﬃciency. However, analysing all the methods that couldpotentially be employed in order to tackle exergy losses is not the topic of this current study. 5. CONCLUSIONSThis study focused on the exergy behaviour of four (4) environmentally friendly refrigerantmixtures. All the theory presented is in accordance with all the currently available literature onthe topic of exergy. All the calculations involved were performed with the use of specializedcomputer software and comparisons were made between NIST and Coolpack software in orderto double-check all the results presented. Although the exergy behaviour of these four (4) refrigerant mixtures is generally inferior tothat of their environmentally hazardous predecessors, their use is constantly gainingmomentum, as they can guarantee the highly craved sustainable environmental development. NOMENCLATUREB =anergy amountCOP =coeﬃcient of Performance E =exergy amount Eu =exergy lossese =speciﬁc exergyh =enthalpy m =refrigerant mass ﬂow ratenis =isentropic compression eﬃciencynmotor =compressor motor eﬃciencyP =powerQo =cooling loadQ =rejected heats =entropyTo =temperature of cold space nTo =evaporation temperatureTu =ambient Temperaturez =exergy eﬃciency factor REFERENCESASHRAE. 1997. Fundamentals Handbook. American Society of Heating, Refridgerating and Air-Conditioning Engineers. New York.Baehr HD. 1989. Thermodynamik. Siebente Auﬂage. Berlin/Heidelberg: Springer.Blackmore R, Reddish A. 1996. Global Environmental Issues (2nd edn). Hodder and Stougton: London.Cavallini A. 1995. Working ﬂuids for Mechanical Refrigeration. Proceedings of the 19th International Congress of Refrigeration, vol. IVa. International Institute of Refrigeration: Hague, Netherlands; 25–42.Copyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078
- 12. 1078 A. STEGOU-SAGIA AND N. PAIGNIGIANNISCoolpack Software. Denmark Technical University, Department of Mechanical Engineering, 2001.Holman JP. 1997. Heat Transfer (8th edn). McGraw-Hill: New York.ICI Chemicals and Polymers. 1995. ICI KLEA 134a Engineer’s Tables. Runcorn, Cheshire: England.Moran M, Shapiro H. 1993. Fundamentals of Engineering Thermodynamics (2nd edn). New York: Wiley.NIST Standard Reference Database 23. 1996. NIST Thermodynamic Properties of Refrigerants and Refrigerant Mixtures, Version 5.0.Ozone Secretariat. 2000. ‘Montreal protocol on substances that deplete the ozone layer’, UNEP.Perry RH, Green DW. 1984. Perry’s Chemical Engineering Handbook (6th edn). McGraw-Hill: Singapore.Reid RC, Prausnitz JM, Poling BE. 1988. The Properties of Gases and Liquids (4th edn). McGraw-Hill: Singapore.Smith JM, Van Ness HC. 1975. Introduction to Chemical Engineering Thermodynamics. (3rd edn). McGraw-Hill: New York, Chemical Engineering Series.Stegou-Sagia A. 1997. Thermodynamic property formulations and heat transfer aspects for replacement refrigerants R123 and R134a. International Journal of Energy Research 21:871–884.Stegou-Sagia A, Damanakis M. 1999. Thermophysical Property Formulations for R32/R134a mixtures. International Journal of Applied Thermodynamics 2(3):139–143.Stegou-Sagia A, Damanakis M. 2000. Binary and ternary blends of R134a as alternative refrigerants to R-22. International Journal of Energy Conversion and Management 41:1345–1359.Copyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078

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